The first show ever aired on television was I Love Lucy. No one seems to remember Texaco Star Theater, the show that made Milton Berle a legend. Or Your Show of Shows, which did much the same for Sid Caesar and company. Or Life of Riley. Or The Goldbergs. Or, for that matter, Meet the Press - launching in 1947 and still going strong today, it's the longest-running TV show of any kind.
If a children's show is referenced it'll be Sesame Street. The only Sesame Street characters are Big Bird, Elmo, Bert, Ernie, Cookie Monster, Grover, and Oscar. And sometimes the Count. You won't see Telly, Snuffy, Baby Bear, Zoe, Rosita, Herry, or Abby parodied a lot. There are no human (non-muppet) characters, except maybe Gordon.
For a while in the 80's, the only poet TV characters had ever heard of was Byron. And the only poem he ever wrote was "She walks in beauty like the night..." Which apparently only consisted of that line. Then on an episode of Kate And Allie, a character quotes this line and wrongly attributes it to Keats. The best part? The character in question was a professor of literature.
Reverend Jim from Taxi recites the entire first stanza of 'She Walks in Beauty', but when asked who wrote it says that he doesn't know. Some punk spray-painted it on the side of his van.
The Cosby Show: "Cliff, please let the woman sit down, she's been walking a long time".
Artemus Gordon read 'She Walks in Beauty' on The Wild Wild West (in the '60s.) The show featured a variety of literary allusions, though they are sometimes anachronistic, like when Dr. Loveless (in the early 1870s) quotes "The Ballad of Reading Gaol" by Oscar Wilde, not written until about the turn of the century.
"Stay back or I'll pull a William Burroughs on your leader here." — Buffy, in "New Moon Rising," threatening to kill the Initiative colonel in "New Moon Rising" by referring to the beat poet who shot and killed his lover in a drunken game of William Tell in 1951. In this example, the joke is that no one gets the reference and Buffy has to explain her threat.
"Scream Montresor all you like, pet." — Spike to Buffy, referring to the Edgar Allen Poe story The Cask of Amontillado.
And, finally, a historical reference that actually takes two episodes spaced three seasons apart to complete. Anya has a throwaway line in "Superstar" describing the vengeance wishes she'd enact on wronged women's ex-boyfriends: "I'd wish he was a dog or ugly or in love with President McKinley or something." Three years later, chastising Anya for going soft, Halfrek says: "You were the single-most hard-core vengeance demon on the roster, and everybody knew it. Do I have to mention Mrs. Czolgosz?" President William McKinley was assassinated by a man named Leon Czolgosz. Leon Czolgosz never married. Which is probably an even smaller reference pool.
Just before a big battle Buffy gives a rather lackluster pep talk followed by Spike claiming it was "not exactly the St Crispin's Day Speech" which was only understood by Giles, the only other British person there and the only one, except maybe Willow, likely to have read Henry V.
Giles: We few, we merry few.
Spike: We band of buggered.
Lampshaded in an episode of Buffy the Vampire Slayer. Vamps are preying on college freshmen, killing them and stealing everything from their dorms. They have a running contest to see which artist has the most posters: Monet or Klimt. Monet is winning, if only because the only Klimt people have posters of is The Kiss.
Not only is Inspector Morse more than knowledgeable of classical music and opera, so are the writers on the show, leading to the use of works far outside the limits of this trope in the mysteries, and obscure jokes that only viewers with an interest in music will ever get.
Blackadder was full of obscure historical jokes, particularly in the third series.
In Doctor Who, when they travel to the past, they only hit relatively big events, but a lot of the events are obscure enough that most people only vaguely remember hearing of them in school.
The episode "Midnight" in the new series 4 has a passenger start chanting a stanza from the poem "Goblin Market" by Christina Rossetti.
In "The Unicorn and the Wasp," when they visit Agatha Christie, Donna mentions The Murder on the Orient Express and Miss Marple. Christie hadn't created either of those yet. The reason the episode was created was because of the distinct cover of Death in the Clouds featuring a giant wasp.
Rose was once referred to as a "tim'rous beasty" in an episode set in Scotland.
"The Impossible Astronaut"/"Day of the Moon", featuring Richard Nixon, only hints at Watergate toward the end, being set near the beginning of Tricky Dick's term.
While Mystery Science Theater 3000 has plenty of the more common ones, they fit in plenty of less common references, often to the area that they live in.
As an extreme example, Mike and the bots pile on so many Chicagoland references in the final act of Beginning of the End that if you aren't familiar with the region you'll probably be bored to tears.
The Hamlet episode had lots of increasingly obscure Shakespeare references, including a few cracks about seating arrangements at the Globe theater.
Servo can't see a frog without making the (Ancient Greek!) frog noise from Aristophanes' The Frogs, and then there was the time (in The Deadly Bees) that Mike said, "This must be the 'bee-loud glade' that Yeats spoke of."
Stargate Atlantis takes place in the Pegasus galaxy. And yes, it actually exists. In fact there are two galaxies by that name, one 2.7 million light-years away, the other 3 Mly.
Fawlty Towers: "That's not a racket! That's Brahms! Brahms' Third Racket!"
Star Trek is pretty bad for this, but will occasionally surprise. The conclusion of one Voyager episode prominently featured Dante's Vita Nuova.
Psych is an exception to Small References Pools in general; some of the references will fly over the heads of people not born in the 80's or 90's, since Shawn and Gus are well-versed in more obscure media. Lampshading: In an episode, a character refers to Shawn as Iago, to which he responds, "What does the parrot from Aladdin have to do with this?"
Although Beakmans World would a lot of times reference the more famous Famous Dead Guys, quite a few were more obscure. For example, in their segment of the microscope, they skipped using Antonie van Leeuwenhoek (the Father of Microbiology) and went for the more obscure Zacharias Jansen, who though credited with creating the compound microscope is far less well-known than Leeuwenhoek (and the FDG Jansen makes sure the kids know it in no uncertain terms).
The Crane brothers in Frasier easily defy this trope, often discussing fine wine and making semi-obscure references to opera and literature.
Criminal Minds begins and ends most episodes with a quote, and there is a huge variety in the sources for these quotes. Plus, one episode had the team only able to solve a case because of knowledge of Geoffrey Chaucer's poem Parlement of Foules and the John Fowles novel The Collector. Then there's all the obscure knowledge Reid spouts on a regular basis... Also, the serial killers who are referenced as precedent are usually real-life examples, indicating that someone did their homework. Unfortunately played straight with the psychology they feature on the show, which is one massive example of at best only doing half the research.
Ted is a big fan of Pablo Neruda. It would be Small Reference Pool in Latin America, but for the States, it's something special.
In-universe: When asked his favorite Bible verse at a very religious household, Ted says, "Whoa, I don't know, how you choose your favorite passage? It's the Bible, there's so many... great... ones in — that one from Pulp Fiction is pretty good..."
Robin makes a lot of references to Canadian history, media, etc. that nobody gets.
This trope is the point of the British Game ShowPointless. The show's researchers give 100 people a short length of time to name as many things in a certain group as they can (e.g. types of shark, John Grisham novels, Clint Eastwood films), and on the show itself, the contestants have to try to score as few points as possible by giving the answers they think none of the research group has said, with answers no-one said landing you an ideal 0 points. Therefore, the larger the reference pools of the contestants, the better they'll do.
Although She Spies tended to go after mostly pop culture, sometimes a slightly more high-brow reference would pop up. In this case, with a bit of Lampshade Hanging:
Cassie: It looks like something Kandinsky threw up on. What? Dennis Miller's gone, somebody's got to make pretentious semi-obscure references.
On Home Improvement, the well-traveled and learned Wilson constantly referenced the ideas of various philosophers and thinkers, both famous and obscure, and took interest in the odd traditions of obscure cultures. A lot of the humor was derived from Tim, who exemplified Men Are Uncultured, reacting to and being confused by Wilson's knowledge.
Gilmore Girls was rife with obscure music, pop-culture and literary references.
Possible example: The 1966 Batman episode "The Bookworm Turns (While Gotham City Burns)" features a villain called The Bookworm (Roddy McDowall), whose crimes are based on book plots. Most of the books referenced are fairly well-known, but at one point Bookworm, having threatened to "blow up" a valuable book, surprises Batman and Robin not by exploding it, but by making a much larger copy of it. This is obviously a pun on the "blowing up" of photographs, and just might be a hidden reference to the Julio Cortazar short story "Blow Up" (on which, yes, the Michelangelo Antonioni film about enlarging a photograph was based). On the other hand, since that story and the movie based on it were not yet widely known when the episode aired, this might be more of a coincidence than a Genius Bonus.
The very first Joker episode, "The Joker Is Wild," had the Joker disguising himself as Pagliaccio, the white-faced, sobbing clown of the Leoncavallo opera of the same name. Batman even lampshaded this fact, mentioning to Robin that most people would picture the typical circus archetype when they thought of clowns, and Joker was counting on Batman's knowledge of opera when he sent him a Pagliaccio doll as a clue.
Averted in The Big Bang Theory. While the bigger names are more likely to come up (because they are bigger names), the cast of geeks will reference virtually anything big or small, from the last thirty years of geek culture. Played straight in-universe by Penny, who can only pay attention long enough to absorp the larger things.